With the progress of the financial markets, financial innovations come out oneafter another, which provides the hedging tools for investors. Meanwhile, it alsocontributes to the speculation in the financial markets and aggravates the fluctuationand risk of the market. For that matter, financial institutions and financial regulatorspay increasingly more attention to financial risk management. Portfolio optimizationis one of the effective ways to control financial risk, and Portfolio optimizationmethods aiming to minimize the risk call for precise measurement of portfolio risk.Traditionally, risk measures such as variance, VaR are used on the assumption ofmultivariate normal distribution of portfolio returns. However, portfolio returnsdemonstrate asymmetries and tail dependency in most of the cases. Therefore,traditional measurement based on the assumption of multivariate normal distributionmay lead to an inaccurate measurement of the portfolio risk.The multivariate distribution function based on Copula can effectively solve theproblems resulting from the assumption that the portfolio returns follow amultivariate normal distribution, and describe the characters of the distribution ofasset returns more accurately. Currently, most of research and applications of Copulaare mainly about bivariate Copula functions while research and applications ofmultivariate Copula are still with limitations. Since pair Copula constructions basedon vine structures demonstrate high flexibility and advantage in constructingmultivariate distribution, the paper uses pair Copula to describe the inner-dependencestructure of portfolio returns and constructs multivariate distribution of portfolioreturns. As a coherent measure of risk, CVaR has been widely used to optimizeportfolios and measure their risk. CVaR is greatly affected by the tail distribution ofrisk factors, so the paper models tail distributions of the return using EVT in order toget a more accurate measurement of CVaR of the portfolio.Taking the the leptokurtosis, fat tails, volatility clustering and the leverage effectof financial time series into account, the paper builds the semi-parametric marginaldistribution of each asset return’s innovation using GARCH-EVT model, captures theinner-dependence structure between innovations using pair Copula and thenconstructs the multivariate distribution of portfolio returns. Then, combining MonteCarlo,Mean-CVaR is used to optimize the portfolio. Finally, an empirical study of four Indexes from Shanghai Stock Exchange is performed and the result suggests thatpair Copula-GARCH-EVT-CVaR is an effective model to optimize investmentportfolios. |